A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

This question tests the students ability to calculate the area of different 2D shapes given the units and measurements required. The formulae for the areas are available if required but students are encouraged to try to remember them themselves.

The shapes are: a rectangle, a parallelogram, a right-angled triangle, and a trapezium.

Author of gif: Picknick
https://commons.wikimedia.org/wiki/File:Parallelogram_area_animated.gif
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Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

Given the first three terms of a sequence, give a formula for the $n^\text{th}$ term.

In the first sequence, $d$ is positive. In the second sequence, $d$ is negative.

Given sequences with missing terms, find the common difference between terms.

Given the first few terms of an arithmetic sequence, write down its formula, then find a couple of particular terms.

Given the cost and profit, find the selling price

rebelmaths

(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

rebelmaths

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Calculation of modulus, argument, multiplication by complex conjugate, given two complex numbers.

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

Given a 3 x 3 matrix, and two eigenvectors find their corresponding eigenvalues. Also fnd the characteristic polynomial and using this find the third eigenvalue and a normalised eigenvector $(x=1)$.

Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

rebelmaths

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

Given a random variable $X$ normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Question on the exponential distribution involving a time intervals and arrivals application, finding expectation and variance. Also finding the probability that a time interval between arrivals is less than a given period. All parameters and times randomised. 

Normal distribution $X \sim  N(\mu,\sigma^2)$ given. Find $P(a \lt X \lt b)$. Find expectation, variance, $P(c \lt \overline{X} \lt d)$ for sample mean $\overline{X}$.

Provided with information on a sample with sample mean and known population variance, use the z test to either accept or reject a given null hypothesis.

Provided with information on a sample with sample mean and standard deviation, but no information on the population variance, use the t test to either accept or reject a given null hypothesis.

Given a statement in words of a relationship between two variables, write down a corresponding formula. It's marked correct if values satisfying the relationship satisfy the formula, and values not satisfying the relationship don't.

Then, given a value for one of the variables, work out the value of the other one. They're substituted into the formula given in the first part and marked correct if it's satisfied.

Both parts use custom marking algorithms.

A cubic with a maximum and minimum point is given. Question is to determine coordinates of the minimum and maximum point.

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Rounding practice to given decimal places and significant figures.

Round numbers to a given number of significant figures.

Several quadratics are given and students are asked to complete the square.

A static block of given mass is sits on a flat plane with defined static and kinetic friction values. It is pushed with enough force to start it moving - calculate the speed of the block after a given distance.